Question: Solve for $x$ and $y$ using elimination. ${-6x-y = -59}$ ${-5x+y = -40}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-y$ and $y$ cancel out. $-11x = -99$ $\dfrac{-11x}{{-11}} = \dfrac{-99}{{-11}}$ ${x = 9}$ Now that you know ${x = 9}$ , plug it back into $\thinspace {-6x-y = -59}\thinspace$ to find $y$ ${-6}{(9)}{ - y = -59}$ $-54-y = -59$ $-54{+54} - y = -59{+54}$ $-y = -5$ $\dfrac{-y}{{-1}} = \dfrac{-5}{{-1}}$ ${y = 5}$ You can also plug ${x = 9}$ into $\thinspace {-5x+y = -40}\thinspace$ and get the same answer for $y$ : ${-5}{(9)}{ + y = -40}$ ${y = 5}$